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We study the ground state properties and the excitation spectrum of bosonswhich, in addition to a short-range repulsive two body potential, interactthrough the exchange of some dispersionless bosonic modes. The latter induces atime dependent (retarded) boson-boson interaction which is attractive in thestatic limit. Moreover the coupling with dispersionless modes introduces areference frame for the moving boson system and hence breaks the Galileaninvariance of this system. The ground state of such a system is depleted {\itlinearly} in the boson density due to the zero point fluctuations driven by theretarded part of the interaction. Both quasiparticle (microscopic) andcompressional (macroscopic) sound velocities of the system are studied. Themicroscopic sound velocity is calculated up the second order in the effectivetwo body interaction in a perturbative treatment, similar to that of Beliaevfor the dilute weakly interacting Bose gas. The hydrodynamic equations are usedto obtain the macroscopic sound velocity. We show that these velocities areidentical within our perturbative approach. We present analytical results forthem in terms of two dimensional parameters -- an effective interactionstrength and an adiabaticity parameter -- which characterize the system. Wefind that due the presence of several competing effects, which determine thespeed of the sound of the system, three qualitatively different regimes can bein principle realized in the parameter space and discuss them on physicalgrounds.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

Ground-state properties and excitation spectra of non-Galilean-invariant interacting Bose systems